Most investors agree that Prime Minister Shinzo Abe’s monetary and economic stimulus measures have initially paid off, but they remain skeptical when it comes to changes in corporate behavior that need more time to take root.

Critics say companies need to focus more on improving shareholder returns by using capital more efficiently. Many of them also note the lack of outside directors on the boards of Japanese companies.

In the U.S. more than 90% of large listed companies have a majority of independent directors on their boards. A similar composition in Japan might help big companies take a more objective look at their use of resources over the long term.

“I think it’s very important that issues concerning governance are addressed in Japan. Better governance leads to better returns for investors,” said Mats Andersson, chief executive of Fourth Swedish National Pension Fund, which has $38 billion in total investment assets, adding that Japanese companies need to increase the number of independent directors.

Over the past few months, the foreign investor landscape in Japan has shifted. Some hedge funds that profited handsomely from the first leg of the Abenomics rally through May retreated while longer-term asset managers ramped up their Japan exposure as the market lost steam over the summer.

The Nikkei Stock Average rose 80% from November through May and plunged into a bear market in mid-June. The index is now up 16% from its June low.

For the short-termers, the prospect of extra monetary stimulus and a weaker yen made Japanese stocks an easy bet. For longer-term investors, the political stability that came with Mr. Abe’s second national election victory in July, the unveiling of structural reform plans and his ability to execute, for example, a hike in the national sales tax were among factors prompting greater investment in Japanese equities over the next two or three years.

But even for these latecomer asset managers that ramped up their Japan positions after June, the decision to invest more in Japan appears to hinge on corporate change.

Encouraged by Mr. Abe’s economic campaign, Daisuke Nomoto, a senior portfolio manager at Boston-based Columbia Management Investment Advisers LLC who helps manage $4.5 billion in international equities, has increased his fund’s exposure to the Japanese market in recent months. But he’s less confident about making a long-haul bet on Japan.

“I don’t have a strong conviction yet that this will be a sustainable rise in shares. For the past year, it was driven by the government, but what has the private sector done? Nothing yet,” Mr. Nomoto said.

Referring to the current debate over whether Japan should reduce its 38% corporate tax – one of the highest in the industrial world – Mr. Nomoto said tax cuts could be used to prod firms to change. Mr. Abe should grant corporate tax breaks only to companies that can manage to reduce their excessive cash balances through dividend and wage increases as well as spending on research and development.

“This way, the return on equity should rise as low earning cash balances are put to more productive use, which should also lead to higher tax revenues for the government” as the economy expands and household spending picks up on the back of wage increases, Mr. Nomoto said.

U.S. asset management firm Franklin Templeton Investments is more optimistic about the changes spurred by Mr. Abe, but that hasn’t led the firm to significantly increase its exposure to Japanese stocks. Its global equity fund remains 1.4% underweight on Japan versus the MSCI All Country World Index as of the end of August.

“Where we see opportunities for corporate change in Japan is for companies to focus more on productivity and on becoming globally competitive,” said Heather Arnold, Franklin Templeton’s director of research and portfolio manager based in London, during a recent visit to Tokyo to meet with company and government officials.